I just upgraded to 12.04 this weekend, and since the upgrade, whenever the screen is turned off (after 5 min of inactivity), the fan starts to run like crazy, making a lot of noise. When I get back to my computer and the screen is turned on again, it's silent again.

Obviously I can't see what's happening when the screen is off, but leaving top open in a terminal window, I see that compiz is taking 50+% of cpu right after the screen is turned on again. This seems quite an excessive load for compiz, given that the screen is off :).
It quickly goes down to about 5% after that. There are spikes up to about 25% during normal use, but no excessive fan whirring noise.

Additional info: I have a Sony Vaio laptop with an i5 processor and an ATI Radeon video card. I have installed the Additional Drivers for the ATI card, but the problem also occurred when I hadn't installed them yet. I have a dual monitor setup with my laptop screen and a separate monitor connected through VGA in different resolutions. In the Catalyst Control Center, I have set the Display Manger settings to "Multi-display desktop".

I used this exact same set-up in 11.10 with no problems. Also, when I upgraded to 12.04, I did a fresh install, where I cleared the disk before installing Ubuntu. (Although I left the Windows partition intact.)

Any idea what migth be causing this, or, more importantly, how I can fix it? The sound of the fan when I'm not using the computer is really annoying.

(My problem seems to be related to this one, but in my case it only happens when the display is turned off, and also it didn't happen in 11.10, so this issue seems to be different enough to get its own question.)

Questions on Ask Ubuntu are expected to relate to Ubuntu within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.
If this question can be reworded to fit the rules in the help center, please edit the question.